Multiple choice

A shopkeeper sells an item at a loss of $12\dfrac {1}{2}\%$. In order to gain $6\%$ profit, he must increase the selling price by Rs. $92.50$. The cost price of the item is

  1. Rs. $500$
  2. Rs. $ 450$
  3. Rs. $550$
  4. Rs. $600$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let CP = x. Loss 12.5% means SP1 = 0.875x. Profit 6% means SP2 = 1.06x. Difference = 1.06x - 0.875x = 0.185x = 92.50. x = 92.50 / 0.185 = 500.

AI explanation

Let the cost price be X, meaning the initial selling price at a loss of 12 1/2 percent is 0.875X. To make a 6 percent profit, the new selling price must be 1.06X. The difference between the new and old selling prices is 1.06X minus 0.875X, which equals 0.185X. Since this difference is 92.50, solving for X by dividing 92.50 by 0.185 gives a cost price of Rs. 500. The answer is Rs. 500.

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